Solve 24*(7/24+5/6-3/4)

$$24 * ( \frac { 7 } { 24 } + \frac { 5 } { 6 } - \frac { 3 } { 4 } )$$

Evaluate

$$9$$

Solution Steps

Least common multiple of 24 and 6 is 24. Convert \frac{7}{24} and \frac{5}{6} to fractions with denominator 24.

$$24\left(\frac{7}{24}+\frac{20}{24}-\frac{3}{4}\right)$$

Since \frac{7}{24} and \frac{20}{24} have the same denominator, add them by adding their numerators.

$$24\left(\frac{7+20}{24}-\frac{3}{4}\right)$$

Add 7 and 20 to get 27.

$$24\left(\frac{27}{24}-\frac{3}{4}\right)$$

Reduce the fraction \frac{27}{24} to lowest terms by extracting and canceling out 3.

$$24\left(\frac{9}{8}-\frac{3}{4}\right)$$

Least common multiple of 8 and 4 is 8. Convert \frac{9}{8} and \frac{3}{4} to fractions with denominator 8.

$$24\left(\frac{9}{8}-\frac{6}{8}\right)$$

Since \frac{9}{8} and \frac{6}{8} have the same denominator, subtract them by subtracting their numerators.

$$24\times \frac{9-6}{8}$$

Subtract 6 from 9 to get 3.

$$24\times \frac{3}{8}$$

Express 24\times \frac{3}{8} as a single fraction.

$$\frac{24\times 3}{8}$$

Multiply 24 and 3 to get 72.

$$\frac{72}{8}$$

Divide 72 by 8 to get 9.

$$9$$

Factor

$$3^{2}$$